A drugstore uses fixed-order cycles for many of the items it stocks. The manager
ID: 447989 • Letter: A
Question
A drugstore uses fixed-order cycles for many of the items it stocks. The manager wants a service level of .98. The order interval is 11 days, and lead time is 3 days. Average demand for one item is 69 units per day, and the standard deviation of demand is 9 units per day. Given the on-hand inventory at the reorder time for each order cycle shown in the following table. Use Table. Cycle On Hand 1 38 2 13 3 109 Determine the order quantities for cycles 1, 2, and 3: (Round your answers to the nearest whole number) Cycle Units 1 2 3
Explanation / Answer
Given:
A drugstore uses the fixed-order-interval (FOI) model
Service Level = 98%
OI = 11 days
LT = 3 days
d = 69 units/day
standard deviation= 9 units/day
Cycle
On Hand
1
38
2
13
3
109
The z value corresponding to 0.98. The closest probability is .9798, which corresponds to z = 2.05.
Q = d (OI + LT) + z s.d. [OI + LT] - A
where, A = inventory on hand
Cycle 1:
Q = d (OI + LT) + z s.d. [OI + LT] - A
Q = 69 (11 + 3) + 2.05 * 9 [11 + 3]) – 38
Q =1035 – 38 = 997
Cycle 2:
Q = d (OI + LT) + z s.d. [OI + LT] - A
Q = 69 (11 + 3) + 2.05 * 9 [11 + 3]) – 13
Q = 1035 – 13 = 1022
Cycle 3:
Q = d (OI + LT) + z s.d. [OI + LT] - A
Q = 69(11 + 3) + 2.05 * 9 [11 + 3]) – 109
Q = 1035– 109 = 926.
So, Order Quantities for
Cycle 1 = 996
Cycle 2 = 1022
Cycle 3 = 926
Cycle
On Hand
1
38
2
13
3
109
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